MEMS gyros are often approximated as coupled, dual mode, resonant devices that transfer energy between two mechanical modes when subjected to rotational rate. These approximations are two degree-of-freedom (DOF) analyses with a mode-to-mode coupling described by Coriolis, elastic, and damping cross terms. In practice, MEMS gyros often exhibit unused, collateral modes with resonant frequencies close to the gyro's two operational modes. These additional modes provide mechanisms for the transfer of energy that are independent of rotational rate and, as a result, can generate errors in the gyro output. The purpose of this paper is to show the effects that collateral modes have on the bias of coupled-mode rate gyros. In this paper, the conventional 2 DOF analysis is extended into a three DOF model that includes one collateral mode. It is shown that the 3 DOF model is able to predict bias errors where the 2 DOF approach does not.